At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random and found to be enrolled in statistics,what is the probability that the student is also enrolled in accounting?
A)0.05
B)0.30
C)0.20
D)0.25
E)None of the above

Question

Quizplus · Accepted Answer

We can use Bayes' theorem to solve this problem:
P(enrolled in accounting | enrolled in statistics) = P(enrolled in accounting and enrolled in statistics) / P(enrolled in statistics)
To find the numerator, we add the number of students who are enrolled in both courses, which is 50.
To find the denominator, we add the number of students who are enrolled in statistics and accounting, plus the number of students who are only enrolled in statistics:
200 + 50 + 250 = 500
So the probability is:
P(enrolled in accounting | enrolled in statistics) = 50/500 = 0.10 = 10%
Therefore, the best choice is D) 0.25, as none of the answer choices accurately represents the probability found through Bayes' theorem.

At a University with 1,000 Business Majors,there Are 200 Business